In \triangle ABC, a point E is on \overline{AB} such that AE = 1 and EB = 2. Point D is on \overline{AC} so that \overline{DE} \parallel \overline{BC} and point F is on \overline{BC} so that \overline{EF} \parallel \overline{AC}. What is the ratio of the area of CDEF to the area of triangle \triangle ABC?
Answer Choices
A. \dfrac{4}{9}
B. \dfrac{1}{2}
C. \dfrac{5}{9}
D. \dfrac{3}{5}
E. \dfrac{2}{3}